Many different applications are known for tree transducers. These have been used in calculus, other forms of higher mathematics. Tree transducers are used for decidability results in logic, for modeling mathematically the theories of syntax direction translations and program schemata, syntactic pattern recognition, logic programming, term rewriting and linguistics.
Within linguistics, automated language monitoring programs often use probabilistic finite state transducers that operate on strings of words. For example, speech recognition may transduce acoustic sequences to word sequences using left to right substitution. Tree based models based on probabilistic techniques have been used for machine translation, machine summarization, machine paraphrasing, natural language generation, parsing, language modeling, and others.
A special kind of tree transducer, often called an R transducer, operates with its roots at the bottom, with R standing for “root to frontier”. At each point within the operation, the transducer chooses a production to apply. That choice is based only on the current state and the current root symbol. The travel through the transducer continues until there are no more state annotated nodes.
The R transducer represents two pairs, T1 and T2, and the conditions under which some sequence of productions applied to T1 results in T2. This is similar to what is done by a finite state transducer.
For example, if a finite state transition from state q to state r eats symbol A and outputps symbol B, then this can be written as an R production of q(A x0)->B (r x0).
The R transducer may also copy whole trees, transform subtrees, delete subtrees, and other operations.